Jessica Taylor. CS undergrad and Master’s at Stanford; former research fellow at MIRI.
I work on decision theory, social epistemology, strategy, naturalized agency, mathematical foundations, decentralized networking systems and applications, theory of mind, and functional programming languages.
Blog: unstableontology.com
Twitter: https://twitter.com/jessi_cata
Re: d20
If you use Bayesianism + CDT, and the coin has already landed: Yes, you never take the d20 bet.
Why CDT is well-motivated for Bayesianism by default: Because CDT motivates taking bets according to one’s subjective probabilities. Without CDT (or something close), non-Bayesian agents can choose to decline bets that would naively be good according to their subjective probabilities. This makes it harder to apply Dutch book arguments to them (to argue they should be Bayesian). See my recent post, “Simple Dutch books versus Sleeping Beauty halfers”.
As my post suggests, it is worth considering EDT+FNC as a quasi-Bayesian anthropic decision theory, as the main alternative to CDT+SIA. Here’s how EDT+FNC reasons on the d20:
“I have no information other than the problem setup; there is no FNC update to make so far. Evidentially on my choosing Heads, Omega has made it Tails, meaning I lose. Similarly, I lose evidentially on choosing Tails. Evidentially on the d20 bet, I’m not guaranteed to lose. Therefore I should pick the d20 bet.”
So they pick the d20 bet despite assigning at least 50% subjective probability to at least one of Heads and Tails.
Since FNC is not even Bayesian (dynamic inconsistency as pointed out by Stuart Armstrong), Bayesianism does not combine well with EDT. See Stuart Armstrong’s Anthropics: Full Non-indexical Conditioning (FNC) is inconsistent.
I think one route towards finding alternatives to Bayesianism is to consider decision theories with Dutch book resistance and/or ex ante optimality, and think of what probabilities/beliefs go well with them.
Idk what you mean by ‘per’. I’m not sure if you’re asking a basic / intro question about Sleeping Beauty and anthropics, or if you’re expressing a positive attitude that, while you understand the basic ideas here, you believe the answer is ambiguous.
Main question: When you wake up, what is probability that the coin came up heads?
Follow-up question: When you wake up and learn it is Monday, what is the probability that the coin came up heads?
Ah. Yeah, reading the original again, I do see the amnesia drugs are administered on every awakening, and that can affect probabilities! (Since one can reason: “either Heads+Monday, Heads+Tuesday, Tails+Monday, Tails+Tuesday, Tails+Wednesday”, so ‘thirder’/SIA rules will say 2⁄5 heads… until they observe it’s not Wednesday, and then they go back to 1⁄3. )
In that scenario I think my comments still apply. With (a) you’re saying that reality fluid is irrelevant to anthropic probabilities, and that your decision rule matches EDT+FNC. With (b) it seems, to be consistent, you should also say reality fluid is irrelevant to anthropic probabilities, so the question is, why take the Monday bet? It looks like an arbitrary preference that the Tails+Monday meal is more important than the Heads+Monday meal.
I’m not saying “no amnesia drugs at all”, I’m trying to disambiguate whether, if Heads, then she is administered amnesia drugs during Monday night. Similarly, if Tails, is she administered drugs during Tuesday night?
The most straightforward answer to those is “no to both” because that reduces complications of “maybe it is Wednesday?” upon waking up. Which is fine for bank balance purposes. However when reasoning about meals it’s harder because then Monday Beauty might take into account that, since she might not be administered amnesia drugs (in the Heads case), then she is going to remember this meal on Wednesday, and that might affect things.
That’s part of why I brought up shrimp welfare: it means we can assume no amnesia drugs on Heads+Monday night or Tails+Tuesday night.
In case (a) it seems you agree with EDT+FNC and that reality fluid is irrelevant to computing anthropic probabilities, so I don’t see any purpose in computing reality fluid at all. In case (b) it seems, if you are (consistently with (a)) saying reality fluid is irrelevant to computing anthropic probabilities, then reality fluid could only be relevant to the utility function (if it is relevant at all), and then my puzzlement re: this looking like an arbitrary preference (for Heads+Monday meal quality being more important than Tails+Monday meal quality) applies.
More specifically, I’m not convinced computing the reality fluid distribution is helpful for making decisions. If “realityfluid doesn’t directly translate to a posterior probability that has to be ‘overcome’” then why don’t I skip the step of computing realityfluid, and do CDT+SIA or EDT+FNC, or just UDT (compute ex ante optimal policy, consider anthropic probabilities extraneous)?
I’m not sure how relevant Wednesday Beauty’s memories are; we could either imagine she remembers Heads+Monday and Tails+Tuesday, or not. If she doesn’t remember it seems somewhat like shrimp welfare, where if Monday Beauty contributes to a shrimp welfare fund, the shrimp don’t remember being her.
So in the shrimp welfare case (or Wednesday beauty remembers nothing case) it seems you’re agreeing with EDT+FNC which means the reality fluid distribution (SSA / single-halfing) is irrelevant. So we can just skip the reality fluid computation here.
In the meal case, it seems you are using reality fluid as an input to the utility function? You said earlier that reality fluid doesn’t translate to posterior probabilities, in which case, it could only be relevant for the utility function. In which case, I’m not convinced that these are preferences that meet the reasonable person standard.
Let’s accept “Monday Beauty might as well choose for Monday Beauty”. So then it seems her utility function is “meal quality for Monday Beauty”. Since reality fluid is irrelevant for posterior probabilities in your view, this raises the question of why she doesn’t use EDT+FNC to maximize expected meal quality for Monday Beauty. That computation would be as follows: (1) compute FNC probabilities: “50% on Heads+Monday, 50% on Tails+Monday”, (2) apply EDT: “Expected Monday Beauty meal quality given I take the bet < 0, so I reject”. In which case she would reject the bet.
Now, there is a possible utility function which considers meal quality for Heads+Monday Beauty twice as important as meal quality for Tails+Monday Beauty. But it is (a) not reasonable to summarize that as “Monday Beauty might as well choose for Monday Beauty”, (b) I don’t think it meets the reasonable person standard (assuming both meals are being forgotten anyway).
We could also think of a variation of meal quality where these are meals for shrimp, in which case it looks more like the altruistic case. Then the question is: “If you accept the Monday bet for yourself, why do you reject it for shrimp?”. And the possible answer seems to be “Inherently, I value Heads+Monday version of myself having a good meal more than Tails+Monday version of myself having a good meal, whereas I have no such discrimination for meals fed to shrimp given Heads or Tails.”. Which… again, I don’t see the point of, as a preference.
Why shouldn’t Monday Beauty reason exactly that way for the benefit of Wednesday Beauty
My question to you is how you counteract the Heads+Monday > Tails+Monday reality fluid ratio. If there is no good reason for this, then it seems Monday Beauty should accept the Monday bet, because she has 2⁄3 of her posterior reality fluid on Heads+Monday. It seemed you were earlier offering a reason why she should not take the Monday bet even though she has twice as much reality fluid on Heads+Monday as Tails+Monday, and that’s what I’m not convinced by.
You could imagine a different setup
We can distinguish “altruistic utility function” (like caring about Wednesday Beauty as the benefactor, or shrimp welfare, etc) from “hedonistic utility function”. As I said, I don’t see why reality fluid based decision theory would reject the Monday bet in the altruistic case. Let’s analyze the hedonistic case.
Our Dutch books now involve meal quality rather than money. On Sunday, Beauty may accept a meal of quality 0, or the following lottery: “-14 meal quality if Heads, +16 meal quality if Tails”. Assume her utility is linear in meal quality. It seems she should accept this, as the expected change to meal quality is positive.
Now when Beauty learns it is Monday, she may accept a meal of quality 0, or the following lottery: “+11 meal quality if Heads, −19 meal quality if Tails”. Here’s how I’d try to answer this using the “reality fluid” method. She believes there is twice as much reality fluid on Monday+Heads as Monday+Tails. As such the meal quality values should be scaled by reality fluid. And 2*11 > 19. So she should accept the meal lottery on Monday.
But combined, the Sunday and the Monday meal lotteries lead to −3 overall meal quality relative to taking the 0-quality meal on each day.
So in both cases (altruistic or hedonistic goal) it seems like the reality fluid method is going to get Dutch booked? (If you could explain the general method, maybe it would seem less ad hoc to me, and easier to evaluate.)
Not sure how you’re using reality fluid to calculate expected values here. If H-M has 1⁄2 of your reality fluid and T-M has 1⁄4, then after seeing it’s Monday, it looks like you should assign 2⁄3 to H-M in common with single halfing. After that you’re arguing that because of who is a benefactor you should bet as if at 50⁄50 odds? I don’t think I understand or agree.
We could assume the benefactor in either case is Wednesday Beauty, who has more or less money in her bank account. In that case I don’t see a good reason why Monday Beauty should reason, “if it was Tails then my reality fluid gets combined and who I combine with is a benefactor so I should double importance and bet at 50⁄50 odds even though I have twice as much reality fluid in Heads/Monday as Tails/Monday”.
I don’t see how the “short-lived Beauty is a counterfactual that never gets any realityfluid” helps either; naively one would expect that under this assumption, upon learning it’s Monday, you should assign 100% to Heads, which seems clearly wrong (and that’s clearly the wrong betting odds). Also it seems adopting this view would mean dis-believing in one’s own mortality quite generally, as long as there is a sliver of a chance of immortality.
I agree “probabilities over centered worlds” is the right idea
You don’t know if it’s the first awakening when you are asked the main question, the one distinguishing thirders from halfrrs. The follow up question which distinguished halfers from double halfers involes knowing it is Monday (therefore the first awakening). This part is not ambiguous.
Regarding “belief to a particular degree”, the question is what subjective probability to assign. (“There’s no good answer / it’s ambiguous” is a reasonably common answer here.) It relates to questions of how to generalize Bayesian probability theory to imperfect recall situations.
Wrote a post which references this draft
Ah, okay. So we construct two propositions, for upper and lower. It’s not always the case that at least one is inhabited (as
I’ve been thinking about effective topology recently in the form of the category of
Not sure I understand; how would you go from my pathological case (
Ah good catch. Fixed
I assume it’s possible to have homomorphic encryption where the key is verifiable. Like if you randomly guessed it, you would be able to decrypt, and if you guessed wrong, you would know you failed to decrypt. The “key checking process” could even be memory-light. In which case it looks like in a “encrypt → compute → decrypt” process, the “decrypt” can’t be doing consciousness, because it’s a massively parallelizable, memory-light guess-and-check.
Briefly:
I wrote about homomorphically encrypted consciousness. I don’t think it’s paradoxical. I think you could imagine receiving evidence that you were in homomorphic encryption (simulation hypothesis variant). I don’t think the ‘input’ thing is paradoxical. An LLM is receiving something like ‘GPU voltage macrostates’ as input, it doesn’t need to have a felt sense of this.
I wrote Mental causation is not load-bearing, which argues that epiphenomenalism is less central to the epistemic problem, than is lack of intelligible supervenience. (So this is saying that type A physicalism e.g. analytic functionalism can more easily accomodate knowledge of one’s own consciousness states.) Russellian monism can perhaps save mental causation on-paper but seems vulnerable to the standard epistemic objections nonetheless.
Nevertheless I think illusionism has a lot going for it, Keith Frankish seems more reasonable than phenomenal realists I have read such as David Chalmers and Philip Goff. Of course there is a state it is easy to know one is in which is reasonable to call “consciousness” on an ordinary language basis, but this need not qualify as the philosopher’s “phenomenal consciousness” or “qualia”, which they sometimes conceptually analyze as non-physical.
I think the key question is how that epistemology works. A P-colorblind human goes through exactly the same thought processes (at the cogsci & physical levels) as an ordinary human, they get the same neural sense data, they run ‘cogito’ just the same, etc. On a functionalist / physicalist account of epistemology, they have the same awareness/knowledge of the same things, which is trouble for detecting any phenomenal difference.
As I see it, the main non-physicalist response to this sort of “debunking” argument is to posit that phenomenal beliefs are themselves non-physical (e.g. Chalmers does this), and these justify a non-physical ‘acquaintance’ relationship. Chalmersian property dualism is pretty un-constrained in how it can characterize this, so maybe it can escape the debunking attempt.
Russellian monism is intermediate, it’s more constrained than property dualism but less than physicalism. It seems Russellian monists will tend towards a “constitution” view where the qualities “make up” the beliefs so that the beliefs “quote” them, and this provides a different way of viewing the beliefs, rejecting both that they are (a) physical beliefs about physical stuff, (b) physical beliefs that indexically refer to non-physical stuff (e.g. making claims about one’s guardian angel).
This seems sketchy to me, I reject ‘acquaintance’ for similar reasons as why Frankish does, but many non-physicalists find it very compelling. I suppose I could entertain the idea more if I had a better idea of how the epistemic acquaintance relationship is supposed to work in Russellian monism, how the non-physical component of phenomenal beliefs could be modeled formally. My post Inverting qualia with group theory and Yuxi’s Hole argument and inverted qualia both discuss how to model qualia realism as giving ‘gauge-like’ extra-physical factors, though it’s not clear how to make the color qualia realist account more scientifically plausible.
Here’s why I think violating Martingale here is fine: There’s no Dutch book against this violation. If Beauty bets on Sunday in favor of Heads and on Monday in favor of Tails, the Monday bet happens twice if Tails. (This is analogous to ordinary Sleeping Beauty, where an “awakening bet” happens on both Monday and Tuesday given Tails.)
If people think Dutch book resistance is a good argument for Bayesianism (and Martingale updating in the usual case), they should find the Dutch book resistance of SIA / generalized thirding to be a compelling reason to deviate from Martingale.
I imagine a conversation between a Thirder and a Bayesian as follows:
(and similar could go for duplicate scenarios, not just amnesic scenarios)
See my recent post for more on SSSA+SIA resistance to Dutch books.